ACT Integrating Essential Skills Practice

What the test measures

Integrating Essential Skills skills

Recognize and appropriately use the mathematical skills and concepts necessary to solve real-world problems.
Read and understand the words, numbers, symbols, diagrams, tables, and graphs in mathematical texts.
Reason quantitatively.
Identify relationships among quantities.
Organize and analyze data presented in various forms.
Solve real-world problems involving measurement, rates, ratios, percentages, and proportions.
Translate a situation described in words into a mathematical expression, equation, or inequality.
Apply mathematical models to solve problems.
Use properties of numbers and operations.
Use simple algebraic manipulations to solve problems.

Standards basis

ACT College and Career Readiness Standards (Mathematics) — national

How the ACT reports it

ACT’s math test is built around the ACT Mathematics reporting categories and ACT College and Career Readiness Standards rather than a state-specific framework. The official description says these standards are empirically derived and are the focus of ACT assessments, with modeling counted across categories.

Blueprint & weighting

Preparing for Higher Math 57%–60% total; Number and Quantity 7%–10%; Algebra 12%–15%; Functions 12%–15%; Geometry 12%–15%; Statistics and Probability 8%–12%; Integrating Essential Skills 40%–43%; Modeling is reported throughout and overlaps other categories.

Official sources

ACT Description of Math Test
ACT College and Career Readiness Standards
ACT College and Career Readiness Standards Mathematics PDF

Practice by skill

Topics mapped to this domain

Try it now

8 free questions · 0/0 correct

Practice playeasy

In a school zone, a car must travel at a speed of at most $35.0$ miles per hour. A car is traveling at $38.2$ miles per hour. What is the minimum decrease needed in the car's speed, in miles per hour, so that it meets the speed limit?

The speed must be at most $35.0$ miles per hour. The minimum decrease is $38.2 - 35.0 = 3.2\textsf{.}$

Practice playeasy

What value of $n$ satisfies $5n - 8 = 17$ ?

Add $8$ to both sides: $5n = 25$ . Divide both sides by $5$ : $n = 5$ .

Practice playeasy

What is $(-16) \div (-4)$ ?

Result: $4$ .

Practice playmedium

Teen volunteers at a food drive packed supply bags so that each volunteer received the same number of water bottles and the same number of granola bars to distribute. The drive had $56$ water bottles and $84$ granola bars in all. Which could be the number of volunteers?

The number of volunteers must divide both totals. Common factors of $56$ and $84$ greater than $1$ include $2$ , $4$ , $7$ , $14$ , and $28$ . Only $14$ appears among the choices: $56 \div 14 = 4$ bottles and $84 \div 14 = 6$ bars per volunteer.

Practice playeasy

What is $7.04 - 1.68$ ?

$7.04 - 1.68 = 5.36$ .

Practice playeasy

What is $3^{1}\textsf{?}$

Any base to the first power equals itself: $3^{1} = 3\textsf{.}$

Practice playeasy

Write $7 \times 7 \times 7 \times 7$ using an exponent.

The base $7$ appears $4$ times as a factor, so $7 \times 7 \times 7 \times 7 = 7^{4}$ .

Practice playhard

Bus route A leaves the station every $20$ minutes, and bus route B leaves every $30$ minutes. Both buses leave together at noon. Over the next $3$ hours, not counting the noon departure, how many times do both buses leave the station at the same time?

Both buses leave together every least common multiple of $20$ and $30$ minutes. Since the GCF of $20$ and $30$ is $10\textsf{,}$ divide their product by the GCF to get that interval: $\dfrac{20 \times 30}{10}=60$ minutes. In $180$ minutes after noon, the shared departures are at $60\textsf{,}$ $120\textsf{,}$ and $180$ minutes, so there are $3$ additional times.